Cut-off region: -
The transistor is off. There is no conduction between the collector and the emitter.
Active region: -
The transistor is on. The collector current is proportional to and controlled by the base current (Ic=ßIB) and relatively insensitive to VCE. In this region the transistor can be an amplifier.
Saturation region: -
The transistor is on. The collector current varies very little with a change in the fill fully base current in the saturation region. The VCE is small, a few tenths of volt. The collector current is strongly dependent on VCE unlike in the active region. It is desirable to operate transistor switches in or near the saturation region when in their on state.
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